Learning-Based, Safety-Constrained Control from Scarce Data via Reciprocal Barriers

Verginis, Christos K.; Djeumou, Franck; Topcu, Ufuk

doi:10.1109/cdc45484.2021.9682945

Cited by 4 publications

(2 citation statements)

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“…This paper extends our preliminary work [12] in the following directions: firstly, we consider second-order systems allowing position-like safety constraints with respect to x 1 , in contrast to the first-order case of [12]. Secondly, we provide better insight to the proposed solution by relating the estimation error of g with the frequency of the obtained data.…”

Section: Introductionmentioning

confidence: 76%

“…More specifically, we aim to design a control law that achieves x 1 (t) ∈ Int(C), i.e., h(x 1 (t)) > 0, for all t ≥ t 0 , given that x 1 (t 0 ) ∈ Int(C) for a positive t 0 ≥ 0. In our previous work [12] we considered the safety of systems of the form ẋ = f (x) + g(x)u in terms of h(x) > 0, assuming that ∇h(x) ⊤ g(x) is not identically zero, i.e., relative degree one. This, however, does not apply to safety specifications as dictated by (3) for systems of the form (2), whose relative degree is 2, since ∇h(x 1 ) ⊤ g(x) = 0.…”

Section: Consider a System Characterized Bymentioning

confidence: 99%

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Safety-Constrained Learning and Control using Scarce Data and Reciprocal Barriers

Verginis,

Djeumou,

Topcu

2021

Preprint

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We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control. It is based on data obtained online from the current trajectory and the concept of reciprocal barriers. More specifically, it first uses the obtained data to calculate set-valued functions that over-approximate the unknown dynamic terms. For the second step of the algorithm, we design a robust control scheme that uses these functions as well as reciprocal barriers to render the system forward invariant with respect to the safe set. In addition, we provide an extension of the algorithm that tackles issues of controllability loss incurred by the nullspace of the controldirection matrix. The algorithm removes a series of standard, limiting assumptions considered in the related literature since it does not require global boundedness, growth conditions, or a priori approximations of the unknown dynamics' terms.

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Section: Introductionmentioning

confidence: 76%

Section: Consider a System Characterized Bymentioning

confidence: 99%